RESEARCH_REPORT.md

# Spanish — Full Ablation Study & Research Report

Detailed evaluation of all model variants trained on **Spanish** Wikipedia data by [Wikilangs](https://wikilangs.org).

👈 [Back to README](README.md)

## 📋 Repository Contents

### Models & Assets

- Tokenizers (8k, 16k, 32k, 64k)
- N-gram models (2, 3, 4, 5-gram)
- Markov chains (context of 1, 2, 3, 4 and 5)
- Subword N-gram and Markov chains
- Embeddings in various sizes and dimensions (aligned and unaligned)
- Language Vocabulary
- Language Statistics

![Performance Dashboard](visualizations/performance_dashboard.png)

### Analysis and Evaluation

- [1. Tokenizer Evaluation](#1-tokenizer-evaluation)
- [2. N-gram Model Evaluation](#2-n-gram-model-evaluation)
- [3. Markov Chain Evaluation](#3-markov-chain-evaluation)
- [4. Vocabulary Analysis](#4-vocabulary-analysis)
- [5. Word Embeddings Evaluation](#5-word-embeddings-evaluation)
- [6. Morphological Analysis (Experimental)](#6--morphological-analysis-experimental)
- [7. Summary & Recommendations](#7-summary--recommendations)
- [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)
- [Visualizations Index](#visualizations-index)

---
## 1. Tokenizer Evaluation

![Tokenizer Compression](visualizations/tokenizer_compression.png)

![Tokenizer Fertility](visualizations/tokenizer_fertility.png)

![Tokenizer OOV](visualizations/tokenizer_oov.png)

![Total Tokens](visualizations/tokenizer_total_tokens.png)

### Results

| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|------------|-------------|---------------|----------|--------------|
| **8k** | 3.885x | 3.89 | 0.0687% | 4,882,549 |
| **16k** | 4.280x | 4.28 | 0.0756% | 4,432,264 |
| **32k** | 4.603x | 4.60 | 0.0813% | 4,121,359 |
| **64k** | 4.831x 🏆 | 4.83 | 0.0854% | 3,926,906 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Opegrapha es un género de hongos liquenizados de la familia Opegraphaceae. Espec...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁o pe gra p ha ▁es ▁un ▁género ▁de ▁hon ... (+22 more)` | 32 |
| 16k | `▁o pe gra pha ▁es ▁un ▁género ▁de ▁hongos ▁li ... (+18 more)` | 28 |
| 32k | `▁o pe gra pha ▁es ▁un ▁género ▁de ▁hongos ▁li ... (+17 more)` | 27 |
| 64k | `▁o pe gra pha ▁es ▁un ▁género ▁de ▁hongos ▁li ... (+17 more)` | 27 |

**Sample 2:** `Una única familia: Salicaceae. Árboles, arbustos y matas. Numerosos óvulos; 2 ca...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁una ▁única ▁familia : ▁sal ica ceae . ▁árboles , ... (+29 more)` | 39 |
| 16k | `▁una ▁única ▁familia : ▁sal ica ceae . ▁árboles , ... (+24 more)` | 34 |
| 32k | `▁una ▁única ▁familia : ▁sal icaceae . ▁árboles , ▁arbustos ... (+17 more)` | 27 |
| 64k | `▁una ▁única ▁familia : ▁sal icaceae . ▁árboles , ▁arbustos ... (+17 more)` | 27 |

**Sample 3:** `Apogonia es un género de escarabajos. Algunos son plagas de los árboles de durio...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁apo gon ia ▁es ▁un ▁género ▁de ▁esca ra ba ... (+14 more)` | 24 |
| 16k | `▁apo gon ia ▁es ▁un ▁género ▁de ▁esca raba jos ... (+13 more)` | 23 |
| 32k | `▁apo gonia ▁es ▁un ▁género ▁de ▁esca raba jos . ... (+12 more)` | 22 |
| 64k | `▁apo gonia ▁es ▁un ▁género ▁de ▁escarabajos . ▁algunos ▁son ... (+9 more)` | 19 |


### Key Findings

- **Best Compression:** 64k achieves 4.831x compression
- **Lowest UNK Rate:** 8k with 0.0687% unknown tokens
- **Trade-off:** Larger vocabularies improve compression but increase model size
- **Recommendation:** 32k vocabulary provides optimal balance for production use

---
## 2. N-gram Model Evaluation

![N-gram Perplexity](visualizations/ngram_perplexity.png)

![N-gram Unique](visualizations/ngram_unique.png)

![N-gram Coverage](visualizations/ngram_coverage.png)

### Results

| N-gram | Variant | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|--------|---------|------------|---------|----------------|------------------|-------------------|
| **2-gram** | Word | 183,447 | 17.49 | 4,181,700 | 10.2% | 22.2% |
| **2-gram** | Subword | 225 🏆 | 7.82 | 32,676 | 73.3% | 99.3% |
| **3-gram** | Word | 1,817,727 | 20.79 | 12,295,310 | 2.4% | 7.7% |
| **3-gram** | Subword | 1,802 | 10.82 | 237,444 | 31.5% | 76.4% |
| **4-gram** | Word | 7,309,961 | 22.80 | 24,272,836 | 1.0% | 3.5% |
| **4-gram** | Subword | 10,272 | 13.33 | 1,392,210 | 16.3% | 43.2% |
| **5-gram** | Word | 8,151,138 | 22.96 | 17,610,926 | 0.6% | 2.4% |
| **5-gram** | Subword | 43,696 | 15.42 | 4,988,047 | 9.3% | 26.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de la` | 3,764,844 |
| 2 | `en el` | 1,831,679 |
| 3 | `en la` | 1,685,738 |
| 4 | `de los` | 1,321,114 |
| 5 | `a la` | 938,285 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `uno de los` | 141,403 |
| 2 | `de la ciudad` | 115,570 |
| 3 | `la ciudad de` | 108,727 |
| 4 | `referencias enlaces externos` | 100,698 |
| 5 | `la provincia de` | 97,604 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de la provincia de` | 59,022 |
| 2 | `de la ciudad de` | 41,783 |
| 3 | `a lo largo de` | 38,783 |
| 4 | `de la universidad de` | 33,450 |
| 5 | `en la ciudad de` | 31,628 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a lo largo de la` | 12,052 |
| 2 | `cuenta con una población de` | 11,005 |
| 3 | `0 0 0 0 0` | 10,612 |
| 4 | `en los juegos olímpicos de` | 8,927 |
| 5 | `de la segunda guerra mundial` | 8,768 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 52,737,608 |
| 2 | `a _` | 52,540,713 |
| 3 | `_ d` | 41,585,544 |
| 4 | `d e` | 41,490,874 |
| 5 | `s _` | 40,981,306 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 34,910,171 |
| 2 | `d e _` | 27,000,114 |
| 3 | `_ l a` | 16,444,469 |
| 4 | `o s _` | 15,082,263 |
| 5 | `e l _` | 14,921,174 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 25,355,198 |
| 2 | `_ l a _` | 12,685,143 |
| 3 | `_ e n _` | 10,248,634 |
| 4 | `_ e l _` | 9,367,910 |
| 5 | `o _ d e` | 6,941,874 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _ l` | 6,404,305 |
| 2 | `o _ d e _` | 5,587,851 |
| 3 | `s _ d e _` | 5,212,347 |
| 4 | `_ q u e _` | 5,016,845 |
| 5 | `d e _ l a` | 4,732,721 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 225
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~27% of corpus
- **Recommendation:** 4-gram or 5-gram for best predictive performance

---
## 3. Markov Chain Evaluation

![Markov Entropy](visualizations/markov_entropy.png)

![Markov Contexts](visualizations/markov_contexts.png)

![Markov Branching](visualizations/markov_branching.png)

### Results

| Context | Variant | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---------|---------|-------------|------------|------------------|-----------------|----------------|
| **1** | Word | 1.0184 | 2.026 | 16.60 | 2,511,755 | 0.0% |
| **1** | Subword | 1.1686 | 2.248 | 8.74 | 17,433 | 0.0% |
| **2** | Word | 0.4618 | 1.377 | 3.10 | 41,654,830 | 53.8% |
| **2** | Subword | 0.6288 | 1.546 | 4.11 | 152,257 | 37.1% |
| **3** | Word | 0.2403 | 1.181 | 1.67 | 128,974,391 | 76.0% |
| **3** | Subword | 0.6792 | 1.601 | 4.08 | 625,267 | 32.1% |
| **4** | Word | 0.1170 🏆 | 1.084 | 1.24 | 214,851,229 | 88.3% |
| **4** | Subword | 0.6781 | 1.600 | 3.60 | 2,547,890 | 32.2% |

### Generated Text Samples (Word-based)

Below are text samples generated from each word-based Markov chain model:

**Context Size 1:**

1. `de boca juniors al alcanzar sus danzas en el nk con ellos el español y el`
2. `la ribera de jabez aúl en el primer álbum considerada una variante guacara data del encéfalo`
3. `en la pequeña localidad recibió una especie musa valí de megaron del origen suizo enfrentar demandas`

**Context Size 2:**

1. `de la campana de huesca por el proyecto de igual manera considera a los que la rebelión`
2. `en el reino humano ahí habitaban las estribaciones de la flota de la presidencia de manuel fernández`
3. `en la victoria del ejército mexicano las investigaciones arqueológicas fue también del talmud en el ...`

**Context Size 3:**

1. `uno de los testimonios más antiguos independientes de eugène canseliet y tomados exclusivamente de f...`
2. `de la ciudad donde el cadáver yacía aún en el aeropuerto recibió a 4 120 000 de los`
3. `la ciudad de bogotá ya que también fue considerado para ser desarrollado como una expresión profunda...`

**Context Size 4:**

1. `de la provincia de buenos aires de argentina de bienestar social de mallorca cirer toma posesión del...`
2. `de la ciudad de méxico y dentro de la esfera de las tradiciones judías con elementos de culto judío`
3. `a lo largo de la jornada feria barroca a primeros de octubre embarcaron rumbo a la desierta isla de`


### Generated Text Samples (Subword-based)

Below are text samples generated from each subword-based Markov chain model:

**Context Size 1:**

1. `_uien_y_sene_fuá`
2. `e_locipa_y_tatr_`
3. `atrs_a_playblay_`

**Context Size 2:**

1. `e_con_utien_dity,`
2. `a_a_ta_y_carro_el`
3. `_de_tes_perona_pr`

**Context Size 3:**

1. `_de_un_mar_más_all`
2. `de_la_bra_con_el_,`
3. `_la_la_conte,_g._c`

**Context Size 4:**

1. `_de_la_justaventas_`
2. `_la_interés_pequeta`
3. `_en_varie_daño_a_la`


### Key Findings

- **Best Predictability:** Context-4 (word) with 88.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (2,547,890 contexts)
- **Recommendation:** Context-3 or Context-4 for text generation

---
## 4. Vocabulary Analysis

![Zipf's Law](visualizations/zipf_law.png)

![Top Words](visualizations/top20_words.png)

![Coverage Curve](visualizations/vocab_coverage.png)

### Statistics

| Metric | Value |
|--------|-------|
| Vocabulary Size | 1,128,398 |
| Total Tokens | 317,857,480 |
| Mean Frequency | 281.69 |
| Median Frequency | 4 |
| Frequency Std Dev | 33492.75 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 25,424,319 |
| 2 | la | 12,852,916 |
| 3 | en | 10,451,863 |
| 4 | el | 9,561,089 |
| 5 | y | 8,147,125 |
| 6 | a | 5,543,222 |
| 7 | que | 5,130,281 |
| 8 | del | 4,632,587 |
| 9 | los | 4,528,979 |
| 10 | se | 3,615,320 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | drammenselva | 2 |
| 2 | bidagos | 2 |
| 3 | guillenpbro | 2 |
| 4 | peytrequincomisión | 2 |
| 5 | méndezpbro | 2 |
| 6 | ollerhno | 2 |
| 7 | ricamonseñor | 2 |
| 8 | grezillé | 2 |
| 9 | leguedeniau | 2 |
| 10 | lajubaudiere | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9940 |
| R² (Goodness of Fit) | 0.993771 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 44.4% |
| Top 1,000 | 62.8% |
| Top 5,000 | 78.2% |
| Top 10,000 | 84.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9938 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 44.4% of corpus
- **Long Tail:** 1,118,398 words needed for remaining 15.7% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.7898 | 0.3869 | N/A | N/A |
| **mono_64d** | 64 | 0.7625 | 0.3145 | N/A | N/A |
| **mono_128d** | 128 | 0.6860 | 0.2555 | N/A | N/A |
| **aligned_32d** | 32 | 0.7898 🏆 | 0.3861 | 0.5660 | 0.8680 |
| **aligned_64d** | 64 | 0.7625 | 0.3206 | 0.7520 | 0.9260 |
| **aligned_128d** | 128 | 0.6860 | 0.2619 | 0.7960 | 0.9680 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7898 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3209. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 79.6% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.909** | Low formulaic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-a` | aprile, akiya, argumenta |
| `-s` | seifer, seninho, stobar |
| `-ma` | maremmae, maozim, manks |
| `-m` | mizrajíes, moguereños, morganáticas |
| `-c` | captivos, coevolucionarias, clips |
| `-p` | pk3, polistinae, polypetalæ |
| `-t` | tangamanga, tedros, tubariales |
| `-b` | bundesagentur, bitschnau, botrioides |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | lebbeus, tedros, captivos |
| `-a` | tangamanga, akiya, luvana |
| `-o` | kajanto, seninho, ducetio |
| `-e` | aprile, trimble, dumonde |
| `-n` | hazzan, ameln, bebieron |
| `-os` | tedros, captivos, moguereños |
| `-es` | tubariales, emboques, mizrajíes |
| `-as` | coevolucionarias, morganáticas, turillas |

### 6.3 Bound Stems (Lexical Roots)

Bound stems are high-frequency subword units that are semantically cohesive but rarely appear as standalone words. These often correspond to the 'core' of a word that requires inflection or derivation to be valid.

| Stem | Cohesion | Substitutability | Examples |
|------|----------|------------------|----------|
| `iend` | 1.89x | 259 contexts | iendo, fiend, liendo |
| `ient` | 1.55x | 383 contexts | aient, iente, cient |
| `spañ` | 2.35x | 44 contexts | españ, spaña, españa |
| `ació` | 1.84x | 114 contexts | ación, vació, yació |
| `lmen` | 1.79x | 97 contexts | ülmen, olmen, ilmen |
| `aliz` | 1.40x | 288 contexts | aliza, valiz, alizé |
| `ombr` | 1.52x | 179 contexts | ombri, sombr, ombre |
| `resi` | 1.36x | 299 contexts | resis, resid, resit |
| `stru` | 1.34x | 259 contexts | strub, strul, struk |
| `ontr` | 1.45x | 156 contexts | contr, pontro, lontra |
| `renc` | 1.40x | 185 contexts | prenc, renck, frenc |
| `ntre` | 1.41x | 176 contexts | antre, intre, entre |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-a` | `-s` | 162 words | arrianas, alumbrados |
| `-c` | `-s` | 149 words | certhiaxis, corpasinos |
| `-c` | `-a` | 139 words | contrarreforma, cusítica |
| `-p` | `-s` | 132 words | phitos, preformados |
| `-a` | `-a` | 118 words | azaña, artemisina |
| `-s` | `-s` | 116 words | subtropicalis, senderistas |
| `-p` | `-a` | 114 words | proteobacteria, prevalescencia |
| `-e` | `-s` | 111 words | estamos, escarpes |
| `-t` | `-s` | 94 words | tragaluces, thenailles |
| `-c` | `-o` | 88 words | cristofano, calpetano |

### 6.5 Recursive Morpheme Segmentation

Using **Recursive Hierarchical Substitutability**, we decompose complex words into their constituent morphemes. This approach handles nested affixes (e.g., `prefix-prefix-root-suffix`).

| Word | Suggested Split | Confidence | Stem |
|------|-----------------|------------|------|
| desarrollarlas | **`desarrollar-la-s`** | 7.5 | `la` |
| peptoides | **`peptoi-d-es`** | 7.5 | `d` |
| şemsiruhsar | **`şemsiruh-s-ar`** | 7.5 | `s` |
| zakrisson | **`zakris-s-on`** | 7.5 | `s` |
| caesarobrigenses | **`caesarobrigen-s-es`** | 7.5 | `s` |
| kushiyara | **`kushiy-a-ra`** | 7.5 | `a` |
| ngwempisi | **`ngwempi-s-i`** | 7.5 | `s` |
| hēmitheos | **`hēmith-e-os`** | 7.5 | `e` |
| tsimliansk | **`tsimlian-s-k`** | 7.5 | `s` |
| inculcado | **`inculc-a-do`** | 7.5 | `a` |
| cbgranada | **`cbgran-a-da`** | 7.5 | `a` |
| trespasser | **`trespas-s-er`** | 7.5 | `s` |
| megasares | **`megas-ar-es`** | 7.5 | `ar` |
| programarlas | **`programar-la-s`** | 7.5 | `la` |
| galactano | **`galac-ta-no`** | 7.5 | `ta` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Spanish shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.83x) |
| N-gram | **2-gram** | Lowest perplexity (225) |
| Markov | **Context-4** | Highest predictability (88.3%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

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*Generated by Wikilangs Pipeline · 2026-03-04 06:09:07*